Letter of intent and Solution to Problem 183. Reading between the lines is sometimes easier than reading under them, as this problem by Gary Baylor of Yardley, Pa., demonstrates
Letter of intent Problem 184 — Reading between the lines is sometimes easier than reading under them, as this month’s problem by Gary Baylor of Yardley, Pa., demonstrates.
It was 10:00 p.m. and the chase was on! The agile spy bounded over fences and low rooftops as a pack of policemen, detectives, and representatives of various government agencies huffed after him. Too late! The spy plunged into a wellknown embassy and into diplomatic immunity.
Detective Inspector Schnoop wrung his hands and muttered an oath. A certain nation’s latest international scandal would certainly be the top story of the hour. A scrap of paper dropped by the spy indicated he was about to alert the media. On the paper were the figures:
The chase had been the culmination of a six-monthlong investigation. The embassy had been funding a secret group of agitators who had been traced to four empty houses in a seldom-traveled street. Unfortunately, the police had been unable to ascertain which houses. The numbers on the street ran from 123 to 1075.
Schnoop suddenly stopped in his tracks and stared at the scrap in amazement. Let each letter stand for a unique number between 0 and 7, inclusive — no 8s or 9s. What were the house numbers? Will Schnoop and his cracking of the case be the highlight of the 11:00 p.m. news instead?
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Solution to last month’s problem 183 — You know whose side to take if you answered 1/5ft2. Here’s the not-so-silver lining:
The following is one of the several ways to solve this problem.
Consider the center large square and its right-hand neighbor. Since triangle ABC is a right triangle,
We can find the area of the diamond by finding the areas of the four small triangles that surround it and subtracting their total from the area of the 1 in. x 1 in. square. If we can show that triangle ADE is a right triangle, we solve for the area using similar triangles:
By similar triangles, <DEF is also 26.6 deg.
Since the three angles of a triangle must equal 180 deg, < ADE is 90 deg, and triangle ADE is a right triangle. We can use ratios and known values to determine its area.